A system with charge conservation and lattice translation symmetry has a well-defined filling
ν, which is a real number representing the average charge per unit cell. We show that if ν is …

A fundamental manifestation of the nontrivial correlations of an incompressible fractional
quantum Hall (FQH) state is that an electron added to it disintegrates into more elementary …

In a two-dimensional electron gas under a strong magnetic field, correlations generate
emergent excitations distinct from electrons. It has been predicted that “composite fermions” …

We synthesize and partly review recent developments relating the physics of the half-filled
Landau level in two dimensions to correlated surface states of topological insulators in three …

It is well known that there is a particle-hole symmetry for spin-polarized electrons with two-
body interactions in a partially filled Landau level, which becomes exact in the limit where …

Motivated by the issue of particle-hole symmetry for the composite fermion Fermi sea at the
half-filled Landau level, Son has made an intriguing proposal [Phys. Rev. X 5, 031027 …

Fractional quantum Hall (FQH) system at Landau level filling fraction ν= 5/2 has long been
suggested to be non-Abelian, either Pfaffian (Pf) or antiPfaffian (APf) states by numerical …

Motivated by two independent experiments revealing a resistance minimum at the Landau
level (LL) filling factor ν= 2+ 4/9, characteristic of the fractional quantum Hall effect (FQHE) …

Fascinating structures have arisen from the study of the fractional quantum Hall effect
(FQHE) at the even denominator fraction of $5/2$. We consider the FQHE at another even …

Extensive fractional quantum Hall effect (FQHE) has been observed in graphene-based
materials. Some of the observed fractions are anomalous in that FQHE has not been …